NSM Archive - Boron Nitride (BN) - Mechanical Properties, Elastic Constants, Lattice Vibrations

BN - Boron Nitride

Mechanical Properties, Elastic Constants, Lattice Vibrations

Basic Parameters
Elastic Constants
Acoustic Wave Speeds
Dependence of lattice constants
Phonon Frequencies

Basic Parameters

Zinc Blende crystal structure
    Remarks Referens
Density 3.4870 g cm-3 X-ray
 Soma et al. (1974)
3.450 g cm-3   Rumyantsev et al. (2001)
Hardness 9.5 on the Mohs scale  
Surface microhardness 4500 kg mm-2 300 K, using Knoop's pyramid test Gielisse (1997)
Hexagonal crystal structure
    Remarks Referens
Density 2.18 g cm-3
2.0-2.28 g cm-3		   Madelung (1991)
Rumyantsev et al. (2001)
Hardness 1.5 on the Mohs scale  
Wurtzite crystal structure
Crystal structure Wurtzite Remarks Referens
Density 3.4870 g cm-3    
Surface microhardness 3400 kg mm-2 using Knoop's pyramid test Gielisse (1997)
Wurtzite, Zinc Blende & Hexagonal crystal structure at 300 K
Crystal structure Wurtzite Zinc Blende Hexagonal
Density 3.4870 g cm-3 3.450 g cm-3 2.0-2.28 g cm-3
Bulk modulus 400 GPa 400 GPa 36.5 GPa
Hardness on the Mohs scale   9.5 1.5
Surface hardness 3400 kg mm-2 4500 kg mm-2  

Elastic constants at 300 K.

Zinc Blende BN. Elastic constants at 300 K. [Grimsditch & Zouboulis (1994); see also Shimada et al. (1998)]
C11 820 GPa
C12 190 GPa
C44 480 GPa
Second order elactic moduli, c11 7.120 1012 dyn cm-2 300 K, interpolated from
measured values of other
III-IV compound		 Steigmeier (1963)
Hexagonal BN. Elastic constants at 300 K. [Green et al. (1976), Duclaux et al. (1992)]
C11 750 GPa
C12 150 GPa
C33 32 ± 3 GPa
C44 3 GPa
Wurtzite BN. Elastic constants at 300 K. [Shimada et al. (1998); see also Pesin (1980)]
C11 982 GPa
C12 134 GPa
C13 74 GPa
C33 1077 GPa
C44 388 GPa

Zinc Blende. Bulk modulus (compressibility-1) For T = 300 K
Bs=(C11+2C12)/3 Bs = 400 GPa
Anisotropy factor  
C'=(C11-C12)/2 A = 0.66
Shear modulus  
C'=(C11-C12)/2 C' = 315 GPa
[100] Young's modulus  
Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0= 748 GPa
[100] Poisson ratio  
σo=C12/(C11+C12) σo = 0.19

Wurtzite BN. Bulk modulus (compressibility-1) For T = 300 K
Bs = [ C33(C11 + C11) - 2(C13)2] x [C11+ C12-4C13+ 2C33 ]-1 Bs = 400 GPa

Hexagonal BN. Bulk modulus (compressibility-1) For T = 300 K
Solozhenko & Peun (1997) Bs = 36.5 GPa
BN, Hexagonal. The bulk modulus versus temperature .
Solozhenko & Peun (1997).

Acoustic Wave Speeds

Zinc Blende crystal structure
Wave propagation direction Wave character Expression for wave speed Wave speed (in units of 105 cm/s)
[100] VL (longitudinal) (C11/ρ )1/2 15.4
VT (transverse) (C44/ρ )1/2 11.8
[110] Vl [(C11+Cl2+2C44)/2ρ ]1/2 16.9
Vt|| Vt||=VT= (C44/ρ)1/2 11.8
Vt⊥ [(C11-C12)/2ρ]1/2 9.6
[111] Vl' [(C11+2C12+4C44)/3ρ ]1/2 17.4
Vt' [(C11-C12+C44)/3ρ ]1/2 10.4
Wurtzite crystal structure
Wave propagation direction Wave character Expression for wave speed Wave speed (in units of 105 cm/s)
[100] VL (longitudinal) (C11/ρ )1/2 16.8
VT (transverse, polarization along [001]) (C44/ρ )1/2 10.5
VT (transverse, polarization along [010]) ((C11-C12)/2ρ )1/2 11.0
[001] VL (longitudinal) (C33/ρ )1/2 17.6
VT (transverse ) (C44/ρ )1/2 10.5
Hexagonal crystal structure
Unfortunately, we haven't the information.

The cristalografic direction you can see part Band structure

Dependence of lattice constants

Wurtzite crystal structure
BN, Wurtzite. Lattice constants versus tressure.
Solozhenko et al. (1998).
Hexagonal crystal structure
Zinc Blende crystal structure
Unfortunately, we haven't the information.

Phonon frequencies

Wurtzite crystal structure
A1 - LO 1258 cm-1 Kim et al.(1996);
Karch &Bechstedt (1997);
Shimada et al.(1998)
A1 - TO 1006-1053 cm-1
E1 - LO 1281 cm-1
E1 - TO 1053-1085 cm-1
E2 (low) 476 cm-1
E2 (high) 989 cm-1
BN, Wurtzite BN. Calculated dispersion curves for acoustic and optical branch phonons.
Karch & Bechstedt (1997),
Zinc Blende crystal structure
Phonon wevenumber vLO 1305(1) cm-1 300 K, Raman Sanjurjo et al. (1983)
LO (G) 1285 cm-1   Kim et al.(1996);
Karch &Bechstedt (1997);
Shimada et al.(1998)
Phonon wevenumber vTO 1054.7(6) cm-1 300 K, Raman Sanjurjo et al. (1983)
TO (G) 1000-1082 cm-1   Kim et al.(1996);
Karch &Bechstedt (1997);
Shimada et al.(1998)
BN, Zinc Blende . Calculated dispersion curves for acoustic and optical branch phonons.
Karch & Bechstedt (1997),
Hexagonal crystal structure
E2g 49 cm-1 zone center Raman mode Hoffman et al. (1966)
A2u 770 cm-1
 infrared active mode
E2g 1367 cm-1
zone center Raman mode
E1u 1383 cm-1
 infrared active mode
BN, Hexagonal sheet. Calculated dispersion curves for acoustic and optical branch phonons.
Miyamoto et al. (1995).
BN, hexagonal. Phonon dispersion relations calculated with the rigid ion model
Sokolovskii (1983)